Modeling Mechanical Property Changes During Heating of Carrot Tissue A Microscale Approach
S. Kadam, A. K Datta
Department of Biological & Environmental Engineering, Cornell University, Ithaca, NY, USA
Transport Model
Overview
Multiscale modeling approaches help to describe mechanical
behavior of materials at different scales. Going down in scales,
there is increasing difficulty in developing suitable model.
Building micro-scale models has been confined by the lack
measurement techniques at such scales and computational
complexity due to structural heterogeneity. But development of
such models are necessary as many properties that contribute to
the quality depends on local properties that originates from
tissue heterogeneity.
Therefore, the goal of this study is to develop a quality model of
plant tissue deformation which incorporates micro-scale
geometrical features using carrot as an example. A framework to
derive the dependence of quality with process parameters and
reaction kinetics is developed and discussed.
Factors Affecting Texture
Results
Heat Transfer
Model Validation
Cell wall
Cell vacuole
Moisture Transfer
Tc
cC pc
   (k c  Tc )
t
Tw
 wC pw
   (k w  Tw )
t
Cell vacuole
 c
cc
cc
 Dc
 c
t
1  xc
Cell wall
 c
cw
 Dwcc w
t
Cell membrane
(1)
(2)
Water
potential
k p ( c   w )
J  w
w
x
c  s   p

(4)
(5)
(6)
(a) real tissue geometry
Turgor pressure
(b) uniform honeycomb geometry
Effect of turgor pressure and pectin degradation

Pectin degradation

Solubility of pectin increases as increase in temperature and
cooking time via β-elimination reaction which follows zero
order kinetics
Pn
(7)
k
Vacuole
The rate decrease in modulus decreases with
increase in cooking temperature
(3)
Reaction Kinetics
Pectin Degradation
The model was validated for effective Young’ modulus at
different temperatures
The initial loss of modulus is due to the
loss of turgor pressure
Pectin plays less important role during
initial loss of modulus
t
Ea  1 1 
k  kref  exp 
 
R  Tref T 
Reaction rate
constant
Cell Membrane Cell Wall
Linear relationship between pectin degradation and cell wall
modulus was assumed
(9)
P
Turgid plant cells
Β-elimination at
high temperature
Turgor pressure
(8)
Cell wall modulus
Ecw 
Po
 Eo
Initial cell wall
modulus
Galacturonic acid
Solid Mechanics Model
Effective Young’s Modulus
Tissue
softening
Under uniaxial loading Young’s modulus is obtained by
homogenization
Plant cells after loss of
turgor pressure
  0
Factors Affecting Texture


Water potential prediction
90% water is present inside the vacuole of the cell which is
surrounded by cell membrane and cell wall. Initially cell
membrane is semi-permeable. As the temperature increases,
σ  Dε
  dA
Eeff 
A
(10)
Methodology
cell membrane permeability starts to increase due to formation
of holes in the membrane surrounding the vacuole that leads to
turgor pressure loss
Heating causes thermal degradation of middle lamella pectin
via β-elimination reaction
Pectin Degradation
Summary and Conclusions
Modeling Framework
Pectin
degradation
in cell wall

Image acquisition and analysis
Transport
Model
Turgor pressure
loss


A cooking model that predicts the effective Young’s modulus was
developed using micro-scale geometrical features
Initial texture loss is due the loss in turgor pressure
Pectin degradation in cell wall could predict the texture loss over
time and its contribution to the initial loss is small compared with
turgor pressure loss
Acknowledgements
This project is supported by Agriculture and Food Research Initiative Competitive
Grant No. 2009-65503-05800 from the USDA National Institute of Food and
Agriculture
Solid
Reaction
Kinetics
Mechanics
Model
Swati Kadam
175 Riley Robb Hall
Email: [email protected]
Ph: 607-255-2871
cell wall modulus
Quality Model
Simulated geometry and Boundary conditions
Excerpt from the Proceedings of the 2014 COMSOL Conference in Boston
Ashim Datta
208 Riley Robb Hall
Email: [email protected]
Ph: 607-255-2482